Passivity-based control is a well-established technique for coordinating groups of fully-actuated systems, but existing methods for underactuated systems are limited to groups of homogeneous systems, coordinate synchronization tasks, and to specific applications. We propose a generic distributed control method that enables heterogeneous groups of underactuated and fully-actuated mechanical systems to cooperatively assume desired task-space formations, with or without leaders with constant task-space references.

Extending the method of passivity-based control by interconnection and damping assignment (IDA-PBC) to distributed networks of mechanical systems, we derive matching conditions and control laws to achieve the desired stable group behavior. For a suitable choice of virtual coupling forces between the systems in the task space, we can decouple the matching conditions into three conditions local to each agent, independent of the topology of the undirected and connected network. If these local conditions are satisfied, we show how existing single-system IDA-PBC solutions can be used to construct distributed control laws, thereby enabling distributed control design for a large class of applications.

By shaping the input-output behavior of a system in addition to shaping its total energy, we also show how human operators can interact with groups of underactuated mechanical systems using the proposed distributed control scheme. The procedure is illustrated using simulation studies of networks of unmanned aerial vehicles that can assume formations and dock with underactuated flexible-joint manipulators.